Abstract

Wavelets has been used successfully in various problems in image processing, including inpainting, noise removal, super-resolution image restoration, etc. Wavelets on the sphere have been developed to solve such problems for data defined on the sphere, which arise in numerous applications, including cosmology and geophysics, for example. Segmentation is the process of identifying object outlines within images. There are quite a few efficient algorithms for segmentation that depend on the variational approach and the partial differential equation (PDE) modelling. In this talk, I will introduce a way to extend the tight-frame based segmentation method, automatically identifying tube-like structures such as blood vessels in medical images, to segment images on the sphere. I will also review the Proximal Markov chain Monte Carlo (MCMC) method, and talk about its application in Radio Interferometry.